The A* algorithm proceeds by popping the topmost state \(s_k\)  from the priority queue, with \(k\)  being the depth of the state in the search graph, and applying each acceleration \((a,b)_i \in \mathbb {A}\) in the action set to predict new states \(s_{k+1, i} = \mathcal {P}(s_k, (a,b)_i)\) according to Eq. (REF ). In the following, we drop the index \(i\)  and just refer to a successor state \(s_{k+1}\) . Note that our state space is continuous and we refrain from using a state lattice [1]}, or snapping \(s_{k+1}\)  to a grid. We designed the state space to be continuous and maintain a table for closing states where we look up \(s_{k}\)  and ignore it if its cell is already closed. If not, we close the cell. We also ignore all \(s_{k+1}\)  that fall into a closed cell. The closed table coincides with the local map and has a cell size of 5 cm and 0.1 radians for the orientation, respectively.
